Private health insurance premiums will increase by an average of 4.84% after the federal government approved insurers’ proposed rises.

The health minister, Greg Hunt, announced the approval on Friday and said it was the lowest in 10 years and lower than any year in the Rudd or Gillard governments.

For a single person the average yearly increase to take effect on 1 April will be about $100, and for families about $200.

The price increase outstrips inflation, which rose 1.5% in the past 12 months, and inflation in the health sector, which registered a 3.7% rise. The lowest premium rise was 2.98%.

A total of 13m Australians have some form of private health insurance. Benefits paid by private health insurers increased 5.4% over the last financial year.

“I realise cost-of-living pressures are a major concern for Australian families,” Hunt said. “I am determined that more can be done to get better value for families.

“As the new health minister, I will work with insurers over the next year to find ways insurers can deliver more value for customers without compromising on the quality of cover.”

On 3AW on Friday, Malcolm Turnbull said Australians would decide on their own circumstances whether to keep private health cover but he would encourage them to do so.

Turnbull noted price rises were lower than under Labor but added “at a time when household budgets are tight, every additional cost hurts”.

Turnbull attributed price rises to inflation, labour costs, health technology like prostheses and private hospital costs.

Health insurance comparison service, iSelect, estimated average premiums have increased by a total of more than 50% since 2010.

“It’s important that policy holders understand that the increase is an average only, with many Australians expected to be hit with increases well above this average, depending on their provider and they type of policy they hold,” iSelect spokeswoman Laura Crowden said.

Last year the Turnbull government approved premium rises of 5.59% on average. About 9,000 people reportedly dropped their private health insurance last year.

Before Friday’s announcement the average increase in premiums under the Abbott and Turnbull governments was 5.99%, although that will now fall to 5.7%.

The average rise under Rudd and Gillard was 5.55%, compared with 6.67% during the last six years of the Howard government.

Private health insurance has been criticised for its value for money, patchy coverage and high gap payments.

The federal government pays about $6bn a year in private health insurance rebates, which the Greens have proposed abolishing.

Single people who earn more than $90,000 or couples earning more than $180,000 are liable to pay a public health surcharge if they do not take out private insurance, which provides an incentive but makes calculating the value of private cover more difficult.

An investigation by Guardian Australia in November found the problems in the private health system went far beyond the cost of premiums.