Question

Bradley borrowed $72,500 in student loans and he has just graduated from Elon University. He earns enough at his new job to allow him to pay $575 per month on the loan. If the annual rate on the student loan is 4.38% (compounded monthly), how long will it take Bradley to pay off his student loans? Specify the number of months to the nearest whole number

Chandler found his dream mountain home, valued at $245,000. He plans to buy a home just like it when he retires in 15 years. Chandler can earn 6.96 percent per year on his investments. Assume that the price of the house will increase 2.25 percent per year for the next 15 years. How much must he invest at the end of each month for the next 15 years to make the purchase at the end of the 15th year?
A. less than $1,015
B. more than $1,015 but less than $1,080
C. more than $1,080 but less than $1,145
D. more than $1,145 but less than $1,210
E. more than $1,210

Answer 1

Bradley :

The number of months is calculated using the NPER function in Excel with these inputs :

rate = 4.38% / 12 (annual rate converted into monthly rate)

pmt = -575 (monthly payment. this is entered as a negative number as it is a cash outflow)

pv = 72,500 (loan amount. this is entered as a positive number as the loan taken is a cash inflow)

NPER is calculated to be 169.24. Rounding off, 169 months is the time taken to repay the loan

Chandler :

Price of home after 15 years = $245,000 * (1 + 2.25%)¹⁵ = $342,070.67

The amount of monthly deposit to invest is calculated using the PMT function in Excel with these inputs :

rate = 6.96% / 12 (annual rate converted into monthly rate)

nper = 15 * 12 (15 years , with 12 monthly investments each year)

pv = 0 (savings at the beginning of the 15-year period is zero)

fv = 342,070.67 (the amount required at the end of 15 years to buy the home)

PMT is calculated to be $1,082.97.  

The monthly investment required is $1,082.97. The answer is C